We present a mathematically rigorous proof and numerical verification of the Maximum Likelihood Degree (ML degree) of colored Gaussian graphical models (symmetries in concentration/precision matrices). Under the 3-vertex path graph 1-2-3, we analyze two key symmetry configurations. First, we prove that tying the endpoint vertex parameters (K_11 = K_33) keeps the ML degree at 1, yielding a rational MLE solved in closed form. Second, we prove that tying the edge parameters (K_12 = K_23) breaks dec

Domain: mathematics
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